A150332 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 1, 0), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 22, 89, 332, 1439, 5844, 26294, 112273, 516921, 2280559, 10663316, 48126719, 227497714, 1043939945, 4974692955, 23116095160, 110835759296, 520079767164, 2505745180909, 11849659256994, 57314210060168, 272756203807085, 1323475014325766, 6331279115043032, 30802509672438818, 147997678506842738

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A323681 A150330 A150331 * A150333 A057787 A217138

Adjacent sequences: A150329 A150330 A150331 * A150333 A150334 A150335

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved